<div>If we study the results of the tables (2 and 3), in which sample sizes
are (40, and 150) and the combinations of the values of (β, γ) = {(1,
2), (2, 1) and (1.5, 1.5)}. Then we get the results that MLM is the
best for the estimation of β and γ. After MLM, the P.E is best for the
estimation of scale and shape parameters of the BL2PFD.</div><div><b>Application and Discussion</b></div><div>In this section, we have analyzed two real life data sets to demonstrate
the performance of BL2PFD. The comparison of the Probability
distributions has been made in all the data sets on the basis of Akaike
information criterion (AIC), the correct Akaike information criterion
(CAIC), Bayesian information criterion (BIC) and Hannan-Quinn
information criterion (HQIC).</div><div>Finally, using the above mentioned criteria’s, our proposed BL2PFD is
better than the different competitor models for the same data sets.</div><div><b>Bladder Cancer Data</b></div><div>We have adopted the data set consisting the remission time of 128
bladder cancer patients to demonstrate the performance of our proposed
BL2PFD. These data were also studied by [23] and [24]. The
remission times in months are given: 0.08, 0.20, 0.40, 0.50, 0.51, 0.81,
0.90, 1.05, 1.19, 1.26, 1.35, 1.40, 1.46, 1.76, 2.02, 2.02, 2.07, 2.09,
2.23, 2.26, 2.46, 2.54, 2.62, 2.64, 2.69, 2.69, 2.75, 2.83, 2.87, 3.02,
3.25, 3.31, 3.36, 3.36, 3.48, 3.52, 3.57, 3.64, 3.70, 3.82, 3.88, 4.18,
4.23, 4.26, 4.33, 4.34, 4.40, 4.50, 4.51, 4.87, 4.98, 5.06, 5.09, 5.17,
5.32, 5.32, 5.34, 5.41, 5.41, 5.49, 5.62, 5.71, 5.85, 6.25, 6.54, 6.76,
6.93, 6.94, 6.97, 7.09, 7.26, 7.28, 7.32, 7.39, 7.59, 7.62, 7.63, 7.66,
7.87, 7.93, 8.26, 8.37, 8.53, 8.65, 8.66, 9.02, 9.22, 9.47, 9.74, 10.06,
10.34, 10.66, 10.75, 11.25, 11.64, 11.79, 11.98, 12.02, 12.03, 12.07,
12.63, 13.11, 13.29, 13.80, 14.24, 14.76, 14.77, 14.83, 15.96, 16.62,
17.12, 17.14, 17.36, 18.10, 19.13, 20.28, 21.73, 22.69, 23.63, 25.74,
25.82, 26.31, 32.15, 34.26, 36.66, 43.01,46.12 ,79.05.</div><div>We have compared our proposed BL2PFD with the Beta Exponentiated Pareto
distribution (BEPD) by McDonald‘s Power function distribution (McPFD) by
[14], Kumaraswamy Power function distribution (KPFD) by [15],
Beta exponentiated Pareto (BEPD) by [23], Marshall-Olkin Power Lomax
distribution (MOPLx) by [25], and Power function distribution (PFD).</div>